(1) Field of the Invention
The present invention is a method for creating frequency dependent structural/acoustic meshes for three dimensional finite element problems in infinite or semi-infinite mediums. The method maps a three dimensional object to a rectilinear acoustic field that can easily be modified for changes in frequency.
(2) Description of the Prior Art
Finite element analysis of structures submerged in an infinite medium are used to determine the stresses acting on prototype undersea hardware. Simple two dimensional axisymetric models are often employed because three dimensional models are too large and cumbersome to create. The most difficult problems in creating meshes for conventional finite element solvers are: (1) the generation of a three dimensional mesh that can accommodate a range of frequency responses without overstepping the memory requirements of the computer; and (2) the creation of a mesh that can capture small details of a structure and also be transmitted to a larger size mesh suitable for low frequency evaluation.
Not all finite element software packages are capable of solving structural acoustic problems. Often preprocessors are used to create elements that can be imported into nonlinear solvers. The preprocessors become slow and inefficient when processing the large number of nodes to be used in a coupled fluid/structure infinite medium analysis. Also the input files they generate require editing before they can be imported into the solver. When the files get too large, they exceed the memory allotment of the editor on the computer. It is more efficient in these cases to generate meshes using the solver program mesh generator.
Finite element software requires that a structure in a free field be surrounded by one wavelength of acoustic medium on all sides. An absorption fluid impedance condition is then placed at the boundaries to prevent reflections in the medium that could affect the structure's response. Another requirement is that the acoustic element length be a minimum of one-sixth of a wavelength for a solution. Good finite element mesh construction dictates that mesh nodes of linear elements have maximum dimensional ratios of 3:1:1. It also dictates that the included angles on quadrilateral and brick elements be greater than 5 degrees and less than 135 degrees. Often a model is desired to be evaluated for a frequency range over 500 Hz for steady state operation. Using the above criteria, a mesh with one-eighth symmetry that could be used at a frequency of 500 Hz would have a maximum element length of 29.5 inches. If this mesh were also to be used at 10 Hz, the mesh would have to extend 5905 inches in three directions. This would result in a model with 7,919,529 elements. Solving a problem of this size at each frequency of interest becomes an expensive task.